Architecture and Mathematics in Ancient Egypt by Corinna Rossi
Cambridge: Cambridge University Press, 2004. Pp. xxii + 280. ISBN
0--521--82954--2. Cloth £60.00
Reviewed by
Sarah Symons
University of Leicester, UK
[email protected]
Ancient Egyptian monuments include some of the most recognizable
architectural elements in the history of design. We seem to acquire
a familiarity with Egyptian style at an early age; and even people
with little interest in ancient history recognize pyramids, obelisks,
and temple pylons as quintessentially Egyptian. The more attuned
eye, looking at tourist knick-knacks or the efforts of interior designers
to produce an Egyptian-themed dining room in a suburban dwelling,
can easily identify items displaying the ‘wrong’ proportions, or an
intrusive Greek column, or hieroglyphs which are clearly gibberish.
The West’s love affair with Egyptian style, which mushroomed
after the discovery of the tomb of Tutankhamen, has produced a
small but pervasive influence on today’s built environment. The
style known as ‘Egyptian Revival’ influenced buildings from cinema
façades to house porches (often introducing wholly fictitious elements
such as coffin-shaped apertures and obelisks balanced on spheres) in
homage to a civilization which was thought to embody in varying
proportions the elegant, the exotic, and the enigmatic.
The edifices on which these modern attempts are modelled have
a particular and revered place in the canon of architectural styles, traditionally presented as the precursors to the great Greek orders. The
Egyptian lotiform columns and massive pylons are often portrayed as
the transition between the primitive, almost accidental, monolithic efforts of societies without the elevated talents of art and geometry, and
the enlightened, graceful classical buildings with which the popular
imagination associates the birth of democracy, science, and modern
civilization. Egypt’s reputation for arcane knowledge and the desire
of enthusiasts to place Egypt as the birthplace of proportion and spatial order are factors which, joined by scholarly interest in the early
C 2005 Institute for Research in Classical Philosophy and Science
(online)
Aestimatio 2 (2005) 11--15
ISSN 1549–4497
All rights reserved
(print)
ISSN 1549–4470
ISSN 1549–4489 (CD-ROM)
SARAH SYMONS
12
development of architecture and construction, have inspired vigorous
investigation about the ‘rules’ on which the architecture was founded
and the level of knowledge and insight that the ancient architects may
have employed.
Corinna Rossi’s book appears at an interesting juncture. The
heady days of lone enthusiasts galloping all over Egypt measuring
and hypothesizing are over; but, in the field of Egyptian architecture,
the conversation about the significance of geometry within Egyptian monumental buildings in general, and a few famous individual
structures in particular, is continuing. Rossi’s book reflects on the
dialogue so far and offers a considered, even cautious, set of observations about the analyses put forward by her predecessors. Her
approach, flavored by her background as an architect, is investigative, practical, and unemotional. The book treats buildings, blocks
of stone, methods, rituals, and plans as items of evidence, viewed
in a cultural context which never becomes overpoweringly symbolic:
‘one must never forget the weight of stone’, as the author warns in
her conclusion.
The book’s central issue, the relationship between architecture
and mathematics, is discussed (following the structure of the book
itself) with reference to proportion; Egyptian drawing, calculating,
and religious practices; and those most mathematical of edifices, the
pyramids. As the author observes in the case of the tomb KV2, for
which a plan has survived, the outcome of the tension between mathematical theory, religious ideals, and construction methods seems
often to have been that
the final result appears to be a compromise between ritual
ideas and practical considerations, which does not seem to
leave room for the idea that dimensions could have been of
specific, numerical interest.
Part 1 discusses the search for a ‘rule’, a set of guidelines which
the ancient architect or site foreman would have used to lay out and
complete important buildings. The approach to identifying the rule
is usually by trying to deduce it from (plans of) Egyptian structures.
Rossi describes several historical attempts at finding geometrical systems based either on polygons (such as pentagons or particular types
of triangles) or on series of numbers (most famously the Fibonacci series) which yield ratios or proportions for room plans, column heights
13
Aestimatio
and placing, and façades. The author details all the problems with
such schemes—lack of accurate plans, questionable reconstructions
of damaged or lost buildings, and the difficulties of working with tiny
drawings where the width of a pencil line could lead to variations of
several feet in real life—before concluding that Alexander Badawy’s
identification [Badawy 1965] of a triangle with proportions 8:5 seems
to have enough evidence of repeated use for Rossi to distinguish it
as ‘the most successful among the geometrical constructions listed
above, whereas all the others may be dismissed without losing any
significant detail.’
Part 2, ‘Ancient Egyptian Sources’, moves away from analysis of
modern plans in order to review the evidence contained within documents and contemporary plans for Egyptian perceptions of space and
geometry. Surviving Egyptian plans are rare and fascinating documents which, while resembling only weakly the accurate and strictly
planar modern architectural working drawings, contain information
about dimensions, relationships between components, and aspects of
both the plan and the elevations. Sources for Egyptian plans and
architectural models are listed and analyzed. For example, comparison of three modern interpretations of a structure depicted on an
Eighteenth Dynasty wooden board [Davies 1917] illustrates the ambiguities which the modern eye finds in the ancient style. Rossi infers
techniques which the architect would have used (a cubit rod to draw
straight lines) and constraints which he accepted when making the
drawing (fitting it to the shape of the drawing surface). She notes
that one was expected to ‘read the labels, not measure the lines’ and
concludes that sources of this type ‘seem to have been just quick
reminders of a few details of a building’. The details would have
been supplied by ‘long consolidated building practice’, the tradition
of craftsmanship and transmitted ideas which we expect from the
conservative Egyptian civilization.
The final section of part 2 is entitled ‘Foundation Rituals’, starting with the ‘stretching of the cord’ ceremony about which the author presents no new conclusions. The issue of astronomical alignment, which one would expect to have appeared by this point, is not
discussed and is mentioned only parenthetically as a factor in establishing the outline of the new building. This is an indication of how
focused the book is on the practical analysis of its central themes.
SARAH SYMONS
14
The third and final part is devoted entirely to pyramids. Here,
Rossi uses data from more than 80 pyramids for which dimensions
are available or can be inferred. The data, complete with references,
notes, and calculated ratios, is presented in the appendix. The range
and distribution over time of the angle of slope (expressed in the
Egyptian units, sekeds) used for pyramids is analyzed. Rossi suggests that some of the slopes may be related to triangles formed by
using ‘Pythagorean triples’ (sets of integers a, b, and c which satisfy
the relationship a2 + b2 = c2 ). The attestation of Pythagorean triples
in ancient Egypt is generally accepted from the third century BC
[Parker 1972] but is contentious before that date, even for the simplest triple, 3-4-5. Sekeds which can be related to triangles based
on Pythagorean triples were used in the Sixth or even the Fourth
Dynasty, and Rossi speculates that choices of pyramid angles lend
weight to the argument that Pythagorean triples were known at that
time. Rossi is herself cautious about drawing this conclusion; but
it must also be noted that the way the seked unit is produced (being related to two side lengths of a triangle) will, within the range
of sekeds such as we see in pyramids, produce some Pythagorean
triple triangles fortuitously. Our own type of circular angular measurement would have been far less likely to result in the spontaneous
appearance of Pythagorean triangles.
In summary, this book provides a detailed examination of a relatively narrow subject area. There are no grand theories emerging, but
instead, a reflective and practical methodology for analysis of past
theories, and guidelines for thinking about present data. Rossi’s
book will appeal to those looking for a coherent and reasoned explanation of controversial topics such as explicit knowledge and use
in ancient times of abstract mathematical and geometrical concepts.
The book also serves as an ideal counterweight to the proliferation of
home-grown ‘temple theories’ available on the internet. Finally, this
book should also find a readership among architects who are interested in the history of building design and construction. The section
containing Egyptian plans and working drawings will in particular
emphasize the antiquity and continuity of their profession.
bibliography
Badawy, A. 1965. Ancient Egyptian Architectural Design: A Study of
the Harmonic System. Berkeley, CA.
15
Aestimatio
Davies, N. de G. 1917. ‘An Architect’s Plan from Thebes’. Journal of
Egyptian Archaeology 4:194--199.
Parker, R. A. 1972. Demotic Mathematical Papyri. London.